This is the html-rendered R markdown file (Rmd) which accompanies the manuscript:
Huber-Huber, C. & Melcher, D. (2020) The behavioural preview effect with faces is susceptible to statistical regularities: Evidence for predictive processing across the saccade. Manuscript submitted for publication.
The code used to generate this file reproduces all statistics and figures in the manuscript from the data which is provided as well on the OSF page of the project (https://osf.io/ty69k/). This html file also contains all supplementary figures and tables and the analysis of the training phase data which is not directly relevant to the study but shows some very interesting insights (credit to an anonymous reviewer). For all background information about the study, however, please refer to the manuscript file.
Figure and table numbers correspond to figures and tables in the manuscript.
Here, we check the average performance across the experiment in the tilt discrimination task. Participants with less than 60% correct responses are excluded assuming that they did not do the task.
partnr Training prop.corr prop.corr<0.60
1: 33 Invalid 0.5191364 TRUE
2: 37 Invalid 0.5322266 TRUE
3: 8 Invalid 0.5430528 TRUE
4: 34 Valid 0.5475709 TRUE
5: 27 Invalid 0.5616438 TRUE
6: 40 Valid 0.5714286 TRUE
7: 18 Invalid 0.6050831 FALSE
8: 12 Invalid 0.6113744 FALSE
9: 19 Valid 0.6174168 FALSE
10: 36 Valid 0.6656863 FALSE
11: 25 Invalid 0.7247796 FALSE
12: 38 Valid 0.7431641 FALSE
13: 29 Invalid 0.7446184 FALSE
14: 22 Invalid 0.7497556 FALSE
15: 16 Invalid 0.7526882 FALSE
16: 15 Valid 0.7563601 FALSE
17: 32 Invalid 0.7608696 FALSE
18: 11 Valid 0.7617647 FALSE
19: 5 Valid 0.7626953 FALSE
20: 3 Invalid 0.7689282 FALSE
21: 17 Valid 0.7763672 FALSE
22: 2 Valid 0.7778865 FALSE
23: 6 Invalid 0.7864838 FALSE
24: 26 Valid 0.8164062 FALSE
25: 39 Invalid 0.8189824 FALSE
26: 9 Valid 0.8258317 FALSE
27: 24 Invalid 0.8406647 FALSE
28: 10 Invalid 0.8437500 FALSE
29: 7 Valid 0.8447266 FALSE
30: 13 Valid 0.8476562 FALSE
31: 28 Valid 0.8554688 FALSE
32: 35 Invalid 0.8563050 FALSE
33: 20 Invalid 0.8631476 FALSE
34: 21 Valid 0.8875855 FALSE
35: 31 Invalid 0.8895406 FALSE
36: 23 Valid 0.8935547 FALSE
37: 4 Invalid 0.8955665 FALSE
38: 41 Invalid 0.8970588 FALSE
39: 14 Invalid 0.9111328 FALSE
40: 30 Valid 0.9149560 FALSE
41: 1 Valid 0.9274510 FALSE
partnr Training prop.corr prop.corr<0.60
Thus, participants excluded are: 33, 37, 8, 34, 27, 40.
Number of participants per training group:
Training
Valid Invalid
17 18
Age:
Min. 1st Qu. Median Mean 3rd Qu. Max.
18.0 20.0 21.0 22.5 24.0 41.0
Gender (0 -> female; 1 -> male):
gender
0 1
25 10
Handedness (0 -> left; 1 -> right):
handedness
0 1
6 29
Eyedness (0 -> left; 1 -> right):
eyedness
0 1
14 21
For details on the model fitting and model comparison approach, see the corresponding Rmd source code file.
Trials in the RT analysis: 12671, i.e. 70.5826649% of a total number of 17952 trials.
| Dependent variable: | |||||
| -1 / Response time [sec] | |||||
| Fitting method: | |||||
| REML | REML | REML | REML | ||
| (1) | (2) | (3) | (4) | ||
| Random effects variances | |||||
| Participant | |||||
| (Intercept) | 0.039 | 0.049 | 0.049 | 0.049 | |
| Target Orientation (In-Up) | 0.002 | 0.002 | 0.002 | ||
| Preview (Inv-Val) | 0.001 | 0.001 | 0.001 | ||
| Trial number | 0.010 | 0.010 | 0.010 | ||
| Target Orientation x Preview | 0.003 | 0.003 | 0.003 | ||
| Target Orientation x Trial number | 0.0001 | 0.0001 | 0.0001 | ||
| Preview x Trial number | 0 | 0 | |||
| Target Orientation x Preview x Trial number | 0 | ||||
| Residual Variance | 0.039 | 0.036 | 0.036 | 0.036 | |
| Fixed effects | |||||
| Target Orientation (In-Up) | 0.033 | 0.037 | 0.037 | 0.037 | |
| (0.007) | (0.010) | (0.010) | (0.010) | ||
| t = 4.675 | t = 3.749 | t = 3.749 | t = 3.749 | ||
| Preview (Inv-Val) | 0.044 | 0.041 | 0.041 | 0.041 | |
| (0.007) | (0.009) | (0.009) | (0.009) | ||
| t = 6.143 | t = 4.549 | t = 4.549 | t = 4.549 | ||
| Training (Inv-Val) | -0.144 | -0.138 | -0.138 | -0.138 | |
| (0.068) | (0.075) | (0.075) | (0.075) | ||
| t = -2.128 | t = -1.831 | t = -1.831 | t = -1.831 | ||
| Trial number | -0.074 | -0.077 | -0.077 | -0.077 | |
| (0.004) | (0.017) | (0.017) | (0.017) | ||
| t = -20.736 | t = -4.388 | t = -4.388 | t = -4.388 | ||
| Target Orientation x Preview | -0.010 | -0.014 | -0.014 | -0.014 | |
| (0.014) | (0.016) | (0.016) | (0.016) | ||
| t = -0.729 | t = -0.841 | t = -0.841 | t = -0.841 | ||
| Target Orientation x Training | 0.010 | 0.002 | 0.002 | 0.002 | |
| (0.014) | (0.020) | (0.020) | (0.020) | ||
| t = 0.696 | t = 0.083 | t = 0.083 | t = 0.083 | ||
| Preview x Training | -0.074 | -0.070 | -0.070 | -0.070 | |
| (0.014) | (0.018) | (0.018) | (0.018) | ||
| t = -5.242 | t = -3.848 | t = -3.848 | t = -3.848 | ||
| Target Orientation x Trial number | 0.016 | 0.013 | 0.013 | 0.013 | |
| (0.007) | (0.007) | (0.007) | (0.007) | ||
| t = 2.269 | t = 1.866 | t = 1.866 | t = 1.866 | ||
| Preview x Trial number | 0.001 | 0.003 | 0.003 | 0.003 | |
| (0.007) | (0.007) | (0.007) | (0.007) | ||
| t = 0.079 | t = 0.425 | t = 0.425 | t = 0.425 | ||
| Training x Trial number | 0.065 | 0.058 | 0.058 | 0.058 | |
| (0.007) | (0.035) | (0.035) | (0.035) | ||
| t = 9.151 | t = 1.676 | t = 1.676 | t = 1.676 | ||
| Target Orientation x Preview x Training | 0.015 | 0.010 | 0.010 | 0.010 | |
| (0.028) | (0.033) | (0.033) | (0.033) | ||
| t = 0.522 | t = 0.300 | t = 0.300 | t = 0.300 | ||
| Target Orientation x Preview x Trial number | 0.007 | 0.012 | 0.012 | 0.012 | |
| (0.014) | (0.014) | (0.014) | (0.014) | ||
| t = 0.486 | t = 0.854 | t = 0.854 | t = 0.854 | ||
| Target Orientation x Training x Trial number | -0.007 | -0.002 | -0.002 | -0.002 | |
| (0.014) | (0.014) | (0.014) | (0.014) | ||
| t = -0.469 | t = -0.122 | t = -0.122 | t = -0.122 | ||
| Preview x Training x Trial number | 0.033 | 0.028 | 0.028 | 0.028 | |
| (0.014) | (0.014) | (0.014) | (0.014) | ||
| t = 2.359 | t = 2.051 | t = 2.051 | t = 2.051 | ||
| Target Orientation x Preview x Training x Trial number | -0.015 | -0.017 | -0.017 | -0.017 | |
| (0.028) | (0.027) | (0.027) | (0.027) | ||
| t = -0.541 | t = -0.618 | t = -0.618 | t = -0.618 | ||
| Grand mean | -1.025 | -1.022 | -1.022 | -1.022 | |
| (0.034) | (0.038) | (0.038) | (0.038) | ||
| t = -30.344 | t = -27.213 | t = -27.213 | t = -27.213 | ||
| Observations | 12,671 | 12,671 | 12,671 | 12,671 | |
| AICc | -4852.342 | -5702.931 | -5700.924 | -5698.916 | |
| Log Likelihood | 2444.198 | 2874.509 | 2874.509 | 2874.509 | |
| Deviance | -4888.396 | -5749.019 | -5749.019 | -5749.019 | |
| Df | 18 | 23 | 24 | 25 | |
| χ2 | 860.623 | 0 | 0 | ||
| χ2 Df | 5 | 1 | 1 | ||
| p | < .001 | 1.000 | 1.000 | ||
| Model is singular | † | † | |||
The table of model comparisons above indicates that the model with the complete random effects structure is singular. Removing the random slope of the highest-order interaction with zero variance, still leads to a singular model. Removing the next zero variance component leads to a model that we call the maximum identifiable model (here Model 2). This model is better than the model without random slopes as can be seen from the model comparison indices in that table.
Figure 2. Estimated marginal means from the maximum identified model on response time data (Model 2). Individual participants’ conditional modes are illustrated with smaller symbols and thin lines connecting the valid and invalid preview points. The preview effect, the difference between valid and invalid preview trials, depended on the training condition. In contrast to valid training (left side), there was no evidence for a preview effect with invalid training (right side, see also Models 2a and 2b below). Note that effect estimates were obtained for the first trial of the test phase. Error bars represent asymptotic confidence intervals.
Figure 3. Fixed effect coefficients of the maximum identified linear mixed model on response times (Model 2). Error bars represent 95% profile confidence intervals. Effect contrasts are given in brackets next to the names of main effects on the y-axis. In-Up: Inverted minus upright; Inv-Val: Invalid minus valid.
| Parameter | Estimate | Std. Error | t value | 2.5 % | 97.5 % |
| ((Intercept)) | -1.022 | 0.038 | -27.213 | -1.095 | -0.948 |
| Target Orientation (In-Up) | 0.037 | 0.010 | 3.749 | 0.018 | 0.056 |
| Preview (Inv-Val) | 0.041 | 0.009 | 4.549 | 0.024 | 0.059 |
| Training (Inv-Val) | -0.138 | 0.075 | -1.831 | -0.285 | 0.009 |
| Trial number | -0.077 | 0.017 | -4.388 | -0.111 | -0.042 |
| Target Orientation x Preview | -0.014 | 0.016 | -0.841 | -0.046 | 0.018 |
| Target Orientation x Training | 0.002 | 0.020 | 0.083 | -0.037 | 0.040 |
| Preview x Training | -0.070 | 0.018 | -3.848 | -0.105 | -0.034 |
| Target Orientation x Trial number | 0.013 | 0.007 | 1.866 | -0.001 | 0.027 |
| Preview x Trial number | 0.003 | 0.007 | 0.425 | -0.010 | 0.016 |
| Training x Trial number | 0.058 | 0.035 | 1.676 | -0.010 | 0.127 |
| Target Orientation x Preview x Training | 0.010 | 0.033 | 0.300 | -0.054 | 0.074 |
| Target Orientation x Preview x Trial number | 0.012 | 0.014 | 0.854 | -0.015 | 0.038 |
| Target Orientation x Training x Trial number | -0.002 | 0.014 | -0.122 | -0.029 | 0.026 |
| Preview x Training x Trial number | 0.028 | 0.014 | 2.051 | 0.001 | 0.055 |
| Target Orientation x Preview x Training x Trial number | -0.017 | 0.027 | -0.618 | -0.070 | 0.037 |
Figure 4. Response times showed an interaction of Training x Preview x Trial Number, which suggested that training with only valid trials resulted in a larger preview effect than training with only invalid trials particularly in the beginning of the test phase. The preview effect then evolved in opposite directions for both training groups. Compared to the invalid training group, the preview effect in the valid training group declined. Dots represent a random sample of half of all individual data points. Trial number was standardized and centered on the first trial of the test phase.
Note, Figure 4 is zoomed-in at the y-axis.
Here we follow up the interaction Preview x Training x Trial Number to see whether the preview effects are significant within the training groups.
| Parameter | Estimate | Std. Error | t value | 2.5 % | 97.5 % |
| ((Intercept)) | -0.953 | 0.056 | -17.112 | -1.065 | -0.841 |
| Target Orientation (In-Up) | 0.036 | 0.013 | 2.799 | 0.011 | 0.061 |
| Preview (Inv-Val) | 0.076 | 0.015 | 5.154 | 0.047 | 0.105 |
| Trial number | -0.106 | 0.030 | -3.525 | -0.166 | -0.045 |
| Target Orientation x Preview | -0.019 | 0.024 | -0.800 | -0.067 | 0.028 |
| Target Orientation x Trial number | 0.014 | 0.009 | 1.524 | -0.004 | 0.032 |
| Preview x Trial number | -0.011 | 0.009 | -1.187 | -0.029 | 0.007 |
| Target Orientation x Preview x Trial number | 0.021 | 0.019 | 1.124 | -0.016 | 0.057 |
| Parameter | Estimate | Std. Error | t value | 2.5 % | 97.5 % |
| ((Intercept)) | -1.091 | 0.051 | -21.520 | -1.193 | -0.989 |
| Target Orientation (In-Up) | 0.038 | 0.015 | 2.563 | 0.009 | 0.067 |
| Preview (Inv-Val) | 0.007 | 0.011 | 0.607 | -0.015 | 0.028 |
| Trial number | -0.047 | 0.019 | -2.535 | -0.084 | -0.010 |
| Target Orientation x Preview | -0.007 | 0.022 | -0.316 | -0.051 | 0.036 |
| Target Orientation x Trial number | 0.012 | 0.011 | 1.053 | -0.011 | 0.034 |
| Preview x Trial number | 0.017 | 0.010 | 1.676 | -0.003 | 0.036 |
| Target Orientation x Preview x Trial number | 0.002 | 0.020 | 0.118 | -0.037 | 0.041 |
The Preview x Training x Trial Number interaction is significant. Note that in the figure illustrating this interaction, the preview effect is the difference between dashed (invalid preview) and solid (valid preview) lines in the direction of the y-axis. If the training phase was valid, there is a preview effect in the beginning of the following test phase which decreases in the course of the test phase. If training phase was invalid, there is a smaller/no preview effect in the beginning of the following test phase which then, compared to the valid training condition, tends to increase. In other words, the influence of training equals across time.
Besides this interaction, there is a significant main effect of Target Orientation. This effect is in the expected direction known from previous research, i.e. faster responses with upright than with inverted targets. The direction of the effect can be seen from the contrasts of the Target Orientation factor and the value of the effect estimate. The contrast is In-Up, meaning inverted minus upright. That means the effect estimate is calculated by subtracing upright target trials from inverted target trials. That means positive values indicate larger dependent variable values for inverted than for upright targets. The dependent variable transformation of -1 / RT before model fitting ensured that larger values still mean slower responses (i.e. maintain the direction of the effect). Thus, given a positive value for the Target Orientation effect estimate () and confidence intervals excluding zero, we can conclude that responses were significanly faster with upright than with inverted targets.
For details on the model fitting and model comparison approach, see the corresponding Rmd source code file.
Trials in the error rate analysis: 15765 , i.e. 87.8175134% of a total number of 17952 trials.
| Dependent variable: | ||||
| Task error (log odds) | ||||
| (5) | (6) | (7) | (8) | |
| Random effects variances | ||||
| Participant | ||||
| (Intercept) | 0.344 | 0.340 | 0.340 | 0.340 |
| Target Orientation (In-Up) | 0.134 | 0.134 | 0.134 | |
| Preview (Inv-Val) | 0.027 | 0.027 | 0.027 | |
| Trial number | 0.032 | 0.032 | 0.032 | |
| Target Orientation x Trial number | 0.043 | 0.043 | 0.043 | |
| Target Orientation x Preview x Trial number | 0.136 | 0.136 | 0.136 | |
| Preview x Trial number | 0 | 0 | ||
| Target Orientation x Preview | 0 | |||
| Residual Variance | 1 | 1 | 1 | 1 |
| Fixed effects | ||||
| Target Orientation (In-Up) | 0.655 | 0.676 | 0.676 | 0.676 |
| (0.085) | (0.107) | (0.107) | (0.107) | |
| t = 7.725 | t = 6.331 | t = 6.331 | t = 6.331 | |
| Preview (Inv-Val) | -0.107 | -0.101 | -0.101 | -0.101 |
| (0.085) | (0.090) | (0.090) | (0.090) | |
| t = -1.265 | t = -1.125 | t = -1.125 | t = -1.125 | |
| Training (Inv-Val) | 0.082 | 0.070 | 0.070 | 0.070 |
| (0.216) | (0.216) | (0.216) | (0.216) | |
| t = 0.381 | t = 0.326 | t = 0.326 | t = 0.326 | |
| Trial number | 0.020 | -0.003 | -0.003 | -0.003 |
| (0.042) | (0.054) | (0.054) | (0.054) | |
| t = 0.463 | t = -0.048 | t = -0.048 | t = -0.048 | |
| Target Orientation x Preview | 0.028 | 0.027 | 0.027 | 0.027 |
| (0.169) | (0.170) | (0.170) | (0.170) | |
| t = 0.166 | t = 0.158 | t = 0.158 | t = 0.158 | |
| Target Orientation x Training | -0.045 | -0.009 | -0.009 | -0.009 |
| (0.170) | (0.213) | (0.213) | (0.213) | |
| t = -0.265 | t = -0.043 | t = -0.043 | t = -0.043 | |
| Preview x Training | -0.156 | -0.160 | -0.160 | -0.160 |
| (0.169) | (0.179) | (0.179) | (0.179) | |
| t = -0.921 | t = -0.892 | t = -0.892 | t = -0.892 | |
| Target Orientation x Trial number | -0.199 | -0.177 | -0.177 | -0.177 |
| (0.084) | (0.093) | (0.093) | (0.093) | |
| t = -2.363 | t = -1.893 | t = -1.893 | t = -1.893 | |
| Preview x Trial number | -0.023 | -0.031 | -0.031 | -0.031 |
| (0.084) | (0.085) | (0.085) | (0.085) | |
| t = -0.267 | t = -0.370 | t = -0.370 | t = -0.370 | |
| Training x Trial number | -0.115 | -0.111 | -0.111 | -0.111 |
| (0.084) | (0.106) | (0.106) | (0.106) | |
| t = -1.363 | t = -1.053 | t = -1.053 | t = -1.053 | |
| Target Orientation x Preview x Training | -0.071 | -0.068 | -0.068 | -0.068 |
| (0.339) | (0.340) | (0.340) | (0.340) | |
| t = -0.210 | t = -0.200 | t = -0.200 | t = -0.200 | |
| Target Orientation x Preview x Trial number | -0.057 | -0.071 | -0.071 | -0.071 |
| (0.169) | (0.182) | (0.182) | (0.182) | |
| t = -0.338 | t = -0.391 | t = -0.391 | t = -0.391 | |
| Target Orientation x Training x Trial number | 0.006 | 0.033 | 0.033 | 0.033 |
| (0.169) | (0.186) | (0.186) | (0.186) | |
| t = 0.034 | t = 0.178 | t = 0.178 | t = 0.178 | |
| Preview x Training x Trial number | 0.027 | 0.022 | 0.022 | 0.022 |
| (0.169) | (0.170) | (0.170) | (0.170) | |
| t = 0.160 | t = 0.127 | t = 0.127 | t = 0.127 | |
| Target Orientation x Preview x Training x Trial number | 0.088 | 0.105 | 0.105 | 0.105 |
| (0.337) | (0.363) | (0.363) | (0.363) | |
| t = 0.261 | t = 0.288 | t = 0.288 | t = 0.288 | |
| Grand mean | -1.538 | -1.543 | -1.543 | -1.543 |
| (0.108) | (0.108) | (0.108) | (0.108) | |
| t = -14.216 | t = -14.257 | t = -14.257 | t = -14.257 | |
| Observations | 15,765 | 15,765 | 15,765 | 15,765 |
| AICc | 14817.779 | 14775.659 | 14777.665 | 14779.671 |
| Log Likelihood | -7391.87 | -7365.797 | -7365.797 | -7365.797 |
| Deviance | 14783.741 | 14731.595 | 14731.595 | 14731.595 |
| Df | 17 | 22 | 23 | 24 |
| χ2 | 52.146 | 0 | 0 | |
| χ2 Df | 5 | 1 | 1 | |
| p | < .001 | 1.000 | 1.000 | |
| Model is singular | † | † | ||
The table of model comparisons above indicates that the model with the complete random effects structure is singular. Removing the random slope of the less interesting component with zero variance, still leads to a singular model. Removing the next zero variance component leads to the maximum identifiable model (Model 6). This model is better than the model without random slopes as can be seen from the model comparison indices in the table above.
Figure 5. Fixed effect coefficients of the maximum identified generalized linear model on task errors (Model 6). Error bars represent 95% profile confidence intervals. Effect contrasts are given in brackets next to the names of main effects on the y-axis. In-Up: Inverted minus upright; Inv-Val: Invalid minus valid.
| Parameter | Estimate | 2.5 % | 97.5 % |
| ((Intercept)) | -1.543 | -1.762 | -1.328 |
| Target Orientation (In-Up) | 0.676 | 0.467 | 0.890 |
| Preview (Inv-Val) | -0.101 | -0.278 | 0.076 |
| Training (Inv-Val) | 0.070 | -0.363 | 0.503 |
| Trial number | -0.003 | -0.114 | 0.102 |
| Target Orientation x Preview | 0.027 | -0.307 | 0.361 |
| Target Orientation x Training | -0.009 | -0.429 | 0.416 |
| Preview x Training | -0.160 | -0.513 | 0.193 |
| Target Orientation x Trial number | -0.177 | -0.359 | 0.012 |
| Preview x Trial number | -0.031 | -0.198 | 0.135 |
| Training x Trial number | -0.111 | -0.325 | 0.102 |
| Target Orientation x Preview x Training | -0.068 | -0.735 | 0.599 |
| Target Orientation x Preview x Trial number | -0.071 | -0.431 | 0.285 |
| Target Orientation x Training x Trial number | 0.033 | -0.331 | 0.405 |
| Preview x Training x Trial number | 0.022 | -0.312 | 0.355 |
| Target Orientation x Preview x Training x Trial number | 0.105 | -0.610 | 0.820 |
Figure S1. The Target Orientation x Trial Number interaction. This interaction is strictly speaking not significant and anyway theoretically not relevant.
Figure S2. Proportion of errors in Training and Preview conditions.
Clearly less task error with upright than with inverted targets. In addition, there is a borderline significant Target Orientation x Trial Number interaction in the direction of a decreasing target orientation effect (inverted minus upright) across the test phase (Figure S1). However, strickly speaking, this effect is not significant and it is theoretically not relevant, so we do not mention it in the paper.
Training influenced the preview effect in response times. In the beginning of the test phase, there was a clear preview effect if participants had trained with only valid trials. However, after invalid training there was no evidence for a preview effect. Moreover, this change in the preview effect equalled during the test phase.
In addition but theoretically not relevant, target face orientation, affected performance leading to slower responses and more errors when target faces were inverted compared to when they were upright.
The experiment consisted of a training and a test phase. For the main manuscript, we only analysed the data of the test phase, because only that phase was relevant. Here, we also analyse the training phase data to get an idea of why the valid training group gave slower responses than the invalid training group at the start of the test phase.
| Dependent variable: | |||||
| -1 / Response time [sec] | |||||
| Fitting method: | |||||
| REML | REML | REML | REML | ||
| (9) | (10) | (11) | (12) | ||
| Random effects variances | |||||
| Participant | |||||
| (Intercept) | 0.047 | 0.045 | 0.045r | 0.045 | |
| Target Orientation (In-Up) | 0.001r | 0.002r | 0.002 | ||
| Trial number | 0.008 | 0.008r | 0.008 | ||
| Target Orientation x Trial number | 0.001r | 0.002r | 0.002 | ||
| Residual Variance | 0.033 | 0.031 | 0.031 | 0.031 | |
| Fixed effects | |||||
| Target Orientation (In-Up) | 0.022 | 0.027 | 0.027 | 0.027 | |
| (0.007) | (0.009) | (0.010) | (0.010) | ||
| t = 3.257 | t = 3.173 | t = 2.649 | t = 2.599 | ||
| Training (Inv-Val) | 0.052 | 0.052 | 0.052 | 0.051 | |
| (0.074) | (0.072) | (0.072) | (0.072) | ||
| t = 0.706 | t = 0.721 | t = 0.718 | t = 0.715 | ||
| Trial number | -0.068 | -0.065 | -0.065 | -0.065 | |
| (0.003) | (0.015) | (0.016) | (0.016) | ||
| t = -20.315 | t = -4.202 | t = -4.184 | t = -4.167 | ||
| Target Orientation x Training | -0.029 | -0.022 | -0.023 | -0.023 | |
| (0.013) | (0.017) | (0.020) | (0.021) | ||
| t = -2.127 | t = -1.277 | t = -1.124 | t = -1.122 | ||
| Target Orientation x Trial number | 0.007 | 0.001 | 0.001 | 0.001 | |
| (0.007) | (0.008) | (0.009) | (0.010) | ||
| t = 1.033 | t = 0.149 | t = 0.138 | t = 0.148 | ||
| Training x Trial number | -0.020 | -0.020 | -0.019 | -0.019 | |
| (0.007) | (0.031) | (0.031) | (0.031) | ||
| t = -2.970 | t = -0.635 | t = -0.625 | t = -0.617 | ||
| Target Orientation x Training x Trial number | 0.041 | 0.034 | 0.035 | 0.035 | |
| (0.013) | (0.016) | (0.019) | (0.019) | ||
| t = 3.078 | t = 2.156 | t = 1.849 | t = 1.854 | ||
| Grand mean | -0.953 | -0.954 | -0.954 | -0.954 | |
| (0.037) | (0.036) | (0.036) | (0.036) | ||
| t = -25.873 | t = -26.559 | t = -26.576 | t = -26.497 | ||
| Observations | 12,334 | 12,334 | 12,334 | 12,334 | |
| AICc | -6660.63 | -7298.309 | -7300.719 | -7296.973 | |
| Log Likelihood | 3340.324 | 3662.169 | 3664.377 | 3667.517 | |
| Deviance | -6680.648 | -7324.338 | -7328.753 | -7335.034 | |
| Df | 10 | 13 | 14 | 19 | |
| χ2 | 643.691 | 4.415 | 6.281 | ||
| χ2 Df | 3 | 1 | 5 | ||
| p | < .001 | .036 | .280 | ||
Figure S3. Training phase data. Fixed effect coefficients of the best maximum identified linear mixed model on response times (Model 11). Effect contrasts are given in brackets next to the names of main effects on the y-axis. In-Up: Inverted minus upright; Inv-Val: Invalid minus valid.
| Parameter | Estimate | Std. Error | t value | 2.5 % | 97.5 % |
| ((Intercept)) | -0.954 | 0.036 | -26.576 | -1.025 | -0.884 |
| Target Orientation (In-Up) | 0.027 | 0.010 | 2.649 | 0.007 | 0.047 |
| Training (Inv-Val) | 0.052 | 0.072 | 0.718 | -0.089 | 0.192 |
| Trial number | -0.065 | 0.016 | -4.184 | -0.095 | -0.035 |
| Target Orientation x Training | -0.023 | 0.020 | -1.124 | -0.063 | 0.017 |
| Target Orientation x Trial number | 0.001 | 0.009 | 0.138 | -0.017 | 0.020 |
| Training x Trial number | -0.019 | 0.031 | -0.625 | -0.080 | 0.041 |
| Target Orientation x Training x Trial number | 0.035 | 0.019 | 1.849 | -0.002 | 0.072 |
Figure S4. Left panel: Response time across trials in the training phase consisting one group of participants of only valid trials and for another group of participants of only invalid trials (Model 11). Right panel: Response time across trials in the test phase which consisted of 50% valid and invalid trials for all participants (right panel, Model 2, identical to Figure 4). Dots represent a random sample of half of all individual data points. Note that trial numbers were standardized and centered on the first trials within each phase.
Note, Figure S4 is zoomed-in at the y-axis.
As can be seen from the model coefficients in Figure S3 and the response time data across trials in Figure S4, participants in the invalid training condition showed numerically, though not significantly, slower response times than the valid training participants in the beginning of the training phase. This difference numerically declined throught the training phase. At the start of the test phase, both groups of participants were about equally fast. Interestingly, at the beginning of the test phase, the invalid training group still showed about the same response time whereas the valid training group showed significantly slower responses.
| Dependent variable: | |||
| Task error (log odds) | |||
| (13) | (14) | (15) | |
| Random effects variances | |||
| Participant | |||
| (Intercept) | 0.316 | 0.539 | 0.539 |
| te1.mm[, “TargOrientIn-Up”] | 0.349 | 0.349 | |
| te1.mm[, “TrialNum.1z”] | 0.269 | 0.269 | |
| te1.mm[, “TargOrientIn-Up:TrialNum.1z”] | 0 | ||
| Residual Variance | 1 | 1 | 1 |
| Fixed effects | |||
| Target Orientation (In-Up) | 0.432 | 0.492 | 0.492 |
| (0.081) | (0.131) | (0.131) | |
| t = 5.304 | t = 3.745 | t = 3.745 | |
| Training (Inv-Val) | 0.183 | 0.158 | 0.158 |
| (0.207) | (0.263) | (0.263) | |
| t = 0.884 | t = 0.600 | t = 0.600 | |
| Trial number | -0.178 | -0.200 | -0.200 |
| (0.042) | (0.098) | (0.098) | |
| t = -4.272 | t = -2.028 | t = -2.028 | |
| Target Orientation x Training | -0.116 | -0.118 | -0.118 |
| (0.163) | (0.262) | (0.262) | |
| t = -0.712 | t = -0.449 | t = -0.449 | |
| Target Orientation x Trial number | -0.107 | -0.058 | -0.058 |
| (0.083) | (0.086) | (0.086) | |
| t = -1.288 | t = -0.675 | t = -0.675 | |
| Training x Trial number | -0.108 | -0.121 | -0.121 |
| (0.083) | (0.197) | (0.197) | |
| t = -1.296 | t = -0.615 | t = -0.615 | |
| Target Orientation x Training x Trial number | -0.073 | 0.016 | 0.016 |
| (0.166) | (0.171) | (0.171) | |
| t = -0.439 | t = 0.094 | t = 0.094 | |
| Grand mean | -1.320 | -1.352 | -1.352 |
| (0.104) | (0.132) | (0.132) | |
| t = -12.736 | t = -10.261 | t = -10.261 | |
| Observations | 15,485 | 15,485 | 15,485 |
| AICc | 14935.761 | 14720.796 | 14722.799 |
| Log Likelihood | -7458.875 | -7349.389 | -7349.389 |
| Deviance | 14917.75 | 14698.779 | 14698.779 |
| Df | 9 | 11 | 12 |
| χ2 | 218.971 | 0 | |
| χ2 Df | 2 | 1 | |
| p | < .001 | 1.000 | |
| Model is singular | † | ||
Figure S5. Training phase data. Fixed effect coefficients of the best maximum identified linear mixed model on error rates (Model 14). Effect contrasts are given in brackets next to the names of main effects on the y-axis. In-Up: Inverted minus upright; Inv-Val: Invalid minus valid.
| Parameter | Estimate | 2.5 % | 97.5 % |
| ((Intercept)) | -1.352 | -1.620 | -1.089 |
| Target Orientation (In-Up) | 0.492 | 0.233 | 0.755 |
| Training (Inv-Val) | 0.158 | -0.373 | 0.688 |
| Trial number | -0.200 | -0.398 | -0.002 |
| Target Orientation x Training | -0.118 | -0.639 | 0.405 |
| Target Orientation x Trial number | -0.058 | -0.226 | 0.110 |
| Training x Trial number | -0.121 | -0.518 | 0.274 |
| Target Orientation x Training x Trial number | 0.016 | -0.320 | 0.352 |
In the training phase error rates, there is an effect of Target Orientation as we know it (less errors with upright than with inverted targets) and an effect of Trial Number with a negative coefficient meaning that errors decrease across the training phase.
The response time data of the training phase provides some evidence that invalid trials were actually surprising. The valid training group saw the invalid trails for the first time in the beginning of the test phase whereas the invalid training group was already used to the invalid trials. At the end of the training phase, both groups were about equally fast, but at the start of the test phase, the valid training group showed significantly slower responses. Moreover, for the valid training group, responses were particularly slowed down for invalid trials (cf. Figure S4 above). This pattern suggests that the invalid trials were indeed unexpected for the valid training group. In contrast, valid trials did not seem to be a big surprise for the invalid training group, supposedly because of the everyday life experience that objects usually do not change during saccades. Credit to an anonymous reviewer for this insight. Error rates did not show any effects worth mentioning; they were simply lower for upright than for inverted targets and they decreased across the training phase.
R version 3.6.1 (2019-07-05)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Catalina 10.15.6
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
locale:
[1] C
attached base packages:
[1] grid stats graphics grDevices utils datasets methods base
other attached packages:
[1] knitr_1.24 citr_0.3.2 stargazer_5.2.2 boot_1.3-23 emmeans_1.4.5 lme4_1.1-21 Matrix_1.2-18 gtable_0.3.0
[9] ggplot2_3.2.1 data.table_1.12.2
loaded via a namespace (and not attached):
[1] gtools_3.8.1 tidyselect_1.1.0 xfun_0.9 reshape2_1.4.3 purrr_0.3.2 splines_3.6.1 lattice_0.20-38 colorspace_1.4-1
[9] vctrs_0.3.4 generics_0.0.2 miniUI_0.1.1.1 htmltools_0.3.6 yaml_2.2.0 rlang_0.4.7 pillar_1.4.2 nloptr_1.2.1
[17] later_0.8.0 glue_1.4.2 withr_2.1.2 plyr_1.8.4 lifecycle_0.2.0 stringr_1.4.0 munsell_0.5.0 mvtnorm_1.0-11
[25] coda_0.19-3 evaluate_0.14 labeling_0.3 httpuv_1.5.1 highr_0.8 Rcpp_1.0.2 xtable_1.8-4 promises_1.0.1
[33] scales_1.0.0 mime_0.7 digest_0.6.20 stringi_1.4.3 dplyr_1.0.2 shiny_1.3.2 tools_3.6.1 magrittr_1.5
[41] lazyeval_0.2.2 tibble_2.1.3 crayon_1.3.4 pkgconfig_2.0.2 MASS_7.3-51.4 estimability_1.3 assertthat_0.2.1 minqa_1.2.4
[49] rmarkdown_1.15 rstudioapi_0.10 R6_2.4.0 nlme_3.1-140 compiler_3.6.1